63.4.29 problem 24

Internal problem ID [12993]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises page 26
Problem number : 24
Date solved : Wednesday, March 05, 2025 at 08:56:36 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} \frac {x^{\prime }+t x^{\prime \prime }}{t}&=-2 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=1/t*(diff(x(t),t)+t*diff(diff(x(t),t),t)) = -2; 
dsolve(ode,x(t), singsol=all);
 

\[ x \left (t \right ) = -\frac {t^{2}}{2}+c_{1} \ln \left (t \right )+c_{2} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 20

ode=1/t*D[t*D[x[t],t],t]==-2; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to -\frac {t^2}{2}+c_1 \log (t)+c_2 \]

✓ Sympy. Time used: 0.217 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(2 + (t*Derivative(x(t), (t, 2)) + Derivative(x(t), t))/t,0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{1} + C_{2} \log {\left (t \right )} - \frac {t^{2}}{2} \]